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Popular Calculus >

area y^2-3x=4,x-y=2

Solution

area

y^{2} - 3 x = 4, x - y = 2

Solution

\frac{343}{18}

+1

Decimal

19.05555 \dots

Solution steps

Isolate

y

for

y^{2} - 3 x = 4 : y = 4 + 3 x, y = - 4 + 3 x

Isolate

y

for

x - y = 2 : y = - 2 + x

f_{1} (x) = 4 + 3 x

f_{2} (x) = - 4 + 3 x

To find the intersection points solve

f_{i} (x) = f_{j} (x)

4 + 3 x = - 4 + 3 x : x = - \frac{4}{3}

4 + 3 x = - 2 + x : x = 7

- 4 + 3 x = - 2 + x : x = 0

= \int_{- \frac{4}{3}}^{0} ∣ f_{1} (x) - f_{2} (x) ∣ d x + \int_{0}^{7} ∣ f_{1} (x) - f_{3} (x) ∣ d x

= \int_{- \frac{4}{3}}^{0} 4 + 3 x - (- 4 + 3 x) d x + \int_{0}^{7} 4 + 3 x - (- 2 + x) d x

\int_{- \frac{4}{3}}^{0} 4 + 3 x - (- 4 + 3 x) d x = \frac{32}{9}

\int_{0}^{7} 4 + 3 x - (- 2 + x) d x = \frac{31}{2}

= \frac{32}{9} + \frac{31}{2}

Simplify

= \frac{343}{18}

Graph

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Frequently Asked Questions (FAQ)

What is area y^2-3x=4,x-y=2 ?
The answer to area y^2-3x=4,x-y=2 is 343/18